<TITLE>prob020: darts tournament</TITLE>
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<H1>prob020: darts tournament</H1>

<TABLE>
<TR> <TD> proposed by
     <TD ALIGN=LEFT> <A HREF="http://www.cs.york.ac.uk/~tw">
          <B>Toby Walsh</B></A> 
          <ADDRESS><a href="mailto:tw@cs.york.ac.uk">
          tw@cs.york.ac.uk</a></ADDRESS>
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<H3> Specification </H3>

<TT>
Dart competitions in pubs often have prizes for the first, second, third
and fourth best throwers. 
What is the order of play for a darts tournament involving
<i>n</i> throwers that:
a) identifies the best <i>k</i> throwers (and their order);
b) has the least number of matches thrown;
c) has the least number of games on each of <i>m</i> dartboards 
(since tournaments typically run in parallel);
d) and is the most exciting (that is, prize
winners should be discovered at the last possible minute 
so that everyone stays drinking beer until the end of the tournament).


</TT>


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